Blockchain-implemented control method and system for controlling an external process or system

ABSTRACT

The invention provides a computer-implemented method and corresponding system which is implemented using an electronic ledger such as a blockchain. This may or may not be the Bitcoin blockchain. The invention can be used to implement, execute and/or control the performance of a task or process. A method according to the invention comprises the steps of generating a blockchain Transaction which comprises: at least one signed input which comprises a value; and at least one modifiable output. It further comprises the step of extracting the value from the signed input and providing it to a portion of logic to obtain a result; and using the result to modify the output of the Transaction. The transaction provides a record and/or representation of the execution of the portion of logic and/or the result. The signed input is provided to the Transaction using an unlocking script. The at least one input is signed using a signature hash type which renders the input as non-modifiable. This may be the signature hash type SIGHASH_NONE. The Transaction may further comprise at least one unsigned input. The unsigned input may be signed after the output has been modified. The unsigned input can be signed using a signature hash type which prevents modification of the whole Transaction, and may be the signature hash type is SIGHASH_ALL. Further the value can be embedded in a public key associated with the signed input; and extracted from the public key so as to provide it to the portion of logic. The portion of logic can be arranged to implement the functionality of a logic gate or combination of gates, such as an AND, NOT, OR, NOR, XOR, IMPLY, NAND, NONIMPLY or XNOR gate. Thus, the invention provides a highly versatile and useful technical approach for implementing tasks using a blockchain.

This invention relates generally to distributed ledger technology (including blockchain related technologies), and in particular the use of a blockchain in implementing, controlling and/or automating a task or process. It may relate to the use of a blockchain or related technology for recording or representing the execution of a portion of logic. This portion of logic may be arranged to implement the functionality of a logic gate, or plurality of logic gates, such as AND, XOR, NOT, OR etc. . . .

It is important to note that in this document we use the term ‘blockchain’ for the sake of convenience and ease of reference because it is currently the most widely known term in this context. However, the term is used herein (including in the claims) to include all forms of electronic, computer-based distributed ledgers, including, but not limited to blockchain and transaction-chain technologies, permissioned and un-permissioned ledgers, shared ledgers and variations thereof.

A blockchain is an electronic ledger which is implemented as a computer-based decentralised, distributed system made up of blocks which in turn are made up of transactions. Each transaction includes at least one input and at least one output. Each block contains a hash of the previous block so that blocks become chained together to create a permanent, unalterable record of all transactions which have been written to the blockchain since its inception. Transactions contain small programs known as scripts embedded into their inputs and outputs, which specify how and by whom the outputs of the transactions can be accessed. On the Bitcoin platform, these scripts are written using a stack-based scripting language.

In order for a transaction to be written to the blockchain, it must be “validated”. Network nodes (miners) perform work to ensure that each transaction is valid, with invalid transactions rejected from the network. Software clients installed on the nodes perform this validation work on an unspent transaction (UTXO) by executing its locking and unlocking scripts. If execution of the locking and unlocking scripts evaluate to TRUE, the transaction is valid and the transaction is written to the blockchain.

The most widely known application of blockchain technology is the Bitcoin ledger, although other blockchain implementations have been proposed and developed. While Bitcoin may be referred to herein for the purpose of convenience and illustration, it should be noted that the invention is not limited to use with the Bitcoin blockchain and alternative blockchain implementations fall within the scope of the invention.

Blockchain technology is most widely known for the use of cryptocurrency implementation. However, in more recent times, digital entrepreneurs have begun exploring both the use of the cryptographic security system Bitcoin is based on, and the data that can be stored on the Blockchain, to implement new systems. It would be highly advantageous if the blockchain could be used for tasks and processes, such as automated control processes, which are not limited to the realm of cryptocurrency. Such solutions would be able to harness the benefits of the blockchain (e.g. a permanent, tamper proof record of events, distributed processing etc) while being more versatile in their applications.

Such an improved solution has now been devised. Thus, in accordance with the present invention there is provided a system and method as defined in the appended claims.

Therefore, in accordance with the invention there may be provided a computer-implemented method of executing a portion of logic. Additionally or alternatively, the invention may be described as a control method. It may control the operation of a hardware and/or software resource. It may control the execution of a computer-implemented process. Additionally or alternatively, the method may provide a technical mechanism for using a blockchain to record or represent the execution, or the result of the execution, of a portion of logic.

The method may comprise the steps:

-   -   generating a blockchain Transaction which comprises:     -   at least one signed input which comprises a value; and     -   at least one modifiable output;         extracting the value from the signed input and providing it to a         portion of logic to obtain a result; and         using the result to modify the output of the Transaction.

The result may be used to modify the output such that the Transaction represents the result. The transaction may provide a record of the execution of the portion of logic. This record may be stored on a blockchain. It may provide a record of the result of the execution. It may provide a record which comprises parameters relating to the execution.

The term ‘blockchain’ is intended to include all forms of electronic, computer-based distributed ledgers including blockchain and transaction-chain technologies, alt-chains, permissioned and un-permissioned ledgers, shared ledgers and variations thereof.

The portion of logic may be a computer-implemented process. It may be arranged to perform a specified task.

The portion of logic may be external to one or both of the Transaction and the blockchain. Furthermore, a Controller (i.e. the owner of the Transaction and the only entity which can update the transaction's outputs after the inputs are signed) may also be external to one or both of the Transaction and the blockchain. The external Controller can apply the portion of logic to the extracted value to obtain the result and communicate with the Transaction to modify the output of the Transaction based on the result. The portion of logic can be representative of a system which is external to one or both of the Transaction and the blockchain and the method further comprises modifying a state of the system based on the modified output of the Transaction. In this way, the invention can be envisaged to utilize the inherent security of the blockchain system to implement, or at least record the state of, external (“off-block”) logic systems thereby extending the functionality and security of the blockchain system to external systems.

The external system can be any system external to the blockchain whose functionality can, for example, be reduced to a mathematical function, algorithm, or portion of logic such as the functionality of a logic gate or a plurality of logic gates. Such systems will generally have one or more inputs and perform one or more operations on the inputs to generate one or more outputs.

Embodiments of the present invention are useful to ensure that a Controller of such a system remains in control of the system and that the system is robust to attack (e.g. hacking) from another entity. From the perspective of the blockchain, a technical problem solved by at least certain embodiments of the present invention is how to utilize the inherent security of a blockchain system for controlling external “off-block” systems. From the perspective of an external system, a technical problem solved by at least certain embodiments of the present invention is how to increase the security of the external system so that it is robust to hack attacks from third parties.

Examples of external systems to which the present invention can be applied are described herein and include: trading platforms; electronic locks; vehicle control systems; sensors; lighting systems; heating/cooling systems; alarm systems; and industrial manufacturing systems. However, these represent a non-exhaustive list and it is important to note that embodiments of the present invention can in principle be applied to introduce the functionality of a blockchain system into any external system which can be represented by one or more inputs, one or more operations on the inputs; and one or more outputs.

The portion of logic may be arranged to implement the functionality of a logic gate or plurality of logic gates. The logic gate may be an AND, NOT, OR, NOR, XOR, IMPLY, NAND, NONIMPLY or XNOR gate.

The method may further comprise the step of submitting the Transaction to a blockchain. The signed input may be provided to the Transaction using an unlocking script.

The at least one input may be signed using a signature hash type which renders the input as non-modifiable. The signature hash type may be SIGHASH_NONE.

The Transaction may further comprise at least one unsigned input.

The method may further comprise the step of submitting the Transaction to a blockchain. It may comprise the step of signing the unsigned input after the output has been modified. The unsigned input may be signed using a signature hash type which prevents modification of the whole Transaction. The signature hash type may be SIGHASH_ALL.

The value may be embedded in a public key associated with the signed input. Additionally or alternatively, it may be extracted from the public key so as to provide it to the portion of logic.

The method may further comprise the step of establishing and/or selecting a protocol and using the protocol to embed the value in the public key. The public key may be used to create a locking script in an intermediate blockchain Transaction.

The method may further comprise the step of submitting the intermediate Transaction to a blockchain.

The value may be embedded in the public key by generating a new public key P′ wherein: P′=P+HASH(value

S)×G

-   -   where:     -   P is a base or initial public key     -   G is an Elliptic Curve function, such as secp256k1     -   x denotes elliptic curve multiplication by scalar; and     -   denotes elliptic curve addition.

The method may further comprise the step of generating a new private key corresponding to the new public key, wherein: new private key V′=V+HASH(value+S)

The value which is embedded in the public key may be selected from a specified range of values.

The invention also provides a corresponding system. The system may be arranged to implement any embodiment of the method described above.

The invention may provide a computer-implemented system comprising:

-   -   at least one computer-based resource arranged to perform the         step(s) of any preceding claim; and     -   a blockchain or other type of electronic ledger. This may be a         distributed ledger.

Any feature described in relation to one aspect or embodiment of the invention may also be used to effect with one or more other aspects/embodiments.

These and other aspects of the present invention will be apparent from and elucidated with reference to, the embodiment described herein. An embodiment of the present invention will now be described, by way of example only, and with reference to the accompany drawings, in which:

FIG. 1 shows an example transaction and the parts which are hashed with SIGHASH_ALL and SIGHASH_NONE

FIG. 2a shows how a function Controller establishes a PubKey Protocol with each Input Source.

FIG. 2b illustrates a scenario wherein an input source has a value to communicate and calculates a value-embedded public key (PubKey) according to its protocol (PubKey protocol).

FIG. 2c illustrates a scenario wherein an input source uses the value-embedded PubKey to create a locking script which is used in one of the outputs of an intermediate transaction.

FIG. 2d illustrates a scenario wherein the Transaction is created; unsigned input from the Controller and each input is added

FIG. 2e illustrates a scenario wherein every input source signs their respective input to the Transaction with signature type SIGHASH_NONE.

FIG. 2f illustrates a scenario wherein the Controller takes the value-embedded PubKey from each Input Source's unlocking scripts in the Transaction and extracts the embedded value based on the associated PubKey protocol

FIG. 2g illustrates a scenario wherein the Controller applies the function to the extracted values, and modifies the transaction output(s) based on the result.

FIG. 2h illustrates a scenario wherein the Controller signs its input using SIGHASH_ALL and submits the transaction to the blockchain.

FIGS. 3 to 8 show blockchain transactions used in accordance with use case example 1 provided below.

FIGS. 9 to 14 show blockchain transactions used in accordance with use case example 2 provided below.

FIGS. 15 to 20 show blockchain transactions used in accordance with use case example 3 provided below.

FIGS. 21a to 25 show blockchain transactions used in accordance with use case example 4 provided below.

FIGS. 26a to 30 show blockchain transactions used in accordance with use case example 5 provided below.

FIGS. 31 to 35 show blockchain transactions used in accordance with use case example 6 provided below.

FIGS. 36a to 40 show blockchain transactions used in accordance with use case example 7 provided below.

FIGS. 41a to 45 show blockchain transactions used in accordance with use case example 7 provided below.

We now provide an illustrative embodiment of the invention. This embodiment includes techniques relating to:

-   -   The establishment of a shared secret and its use in the         generation of new cryptographic keys     -   A mechanism for securely embedding values in Elliptic Curve         public keys;     -   A blockchain-related scheme or solution in which outputs are         conditional upon inputs using a specific signature hash         combination; and     -   The combination of these techniques to provide a novel mechanism         for constructing an externally evaluated function (i.e. external         to the blockchain).

The invention provides a novel and advantageous solution for using a blockchain to implement a function. The blockchain is used to provide a record of the execution of the function and/or a result of its result. A function can be a subroutine or procedure (i.e. a process or portion of logic) which is applied to a set of inputs and returns a set of outputs. In a preferred embodiment, the function is executed ‘off-block’ ie its performance is not blockchain-dependent. The function is performed by a computer-based resource.

A blockchain (e.g. Bitcoin) transaction is a transfer of (e.g. Bitcoin) value which typically references previous transaction outputs as new transaction inputs and dedicates all input values to new outputs. Transactions are not encrypted, so it is possible to browse and view every transaction ever collected into a block. It would be highly advantageous, however, to be able to construct a blockchain transaction which acts as a function, where the transaction output(s) are conditional or dependent on the information embedded in the transaction input(s).

Important aspects of the present invention include (but are not limited to) a method for creating a blockchain transaction that represents a function where:

-   -   Function Input(s) are represented by the public keys used within         the unlocking script of the transaction's input(s)     -   Function Output(s) are represented by the addresses that the         transaction's outputs are sent     -   Function Procedure is evaluated external to the blockchain         transaction     -   The Function Input(s) can be locked in, before applying the         Function logic and updating the Function Output(s)

Thus, the present invention includes the following:

-   -   A technique for the distribution of a secret value; this can be         achieved using methods which employ elliptic curve arithmetic so         that a message can be embedded in private/public keys; in         addition, the Shared Secret can be established across an         unsecure network     -   A technique for securely embedding a value in Elliptic Curve         Public/Private Keys The invention includes a technique for         Secret Value Distribution allowing values to be securely         embedded in elliptic curve public/private cryptographic keys.         The value can be extracted by the receiving party in linear         time, but remains intractable for attackers even if the         parameters communicated to establish the embedding method are         compromised     -   Bitcoin Transaction Outputs which are conditional on Inputs     -   A novel and inventive method which first signs all of a         transaction's inputs except one with SIGHASH_NONE (locks in         inputs), and then signs the remaining input with SIGHASH_ALL         (locks in inputs and outputs). This flow allows for outputs to         be conditioned upon inputs.

The invention will be illustrated via use case examples provided below, in which blockchain (e.g. Bitcoin) transactions can be used to represent the functionality provided by a logic gate.

The invention utilises techniques for embedding a message in cryptographic (public/private) keys, and also for establishing a shared secret. These are described as follows.

Message Embedding

Given:

-   -   Private key V (an integer)     -   Public key P (elliptic curve point)     -   EC generator G (an elliptic curve function)     -   Message M (a value which can be represented as an integer)

It is known in EC arithmetic that:

P = V × G Elliptic Curve multiplication by scalar

If message M is embedded:

V’ = V + M Integer addition P’ = P + M × G Elliptic Curve Point addition

V′ and P′ are the private/public keys with message M embedded

Shared Secret

Given:

-   -   Party A with private key V_(A) and public key P_(A)     -   Party B with private key V_(B) and public key P_(B)     -   EC generator G (an elliptic curve function)

It is known in EC arithmetic that: P _(A) =V _(A) ×G P _(B) =V _(B) ×G

If both parties publish their public key, a shared secret can be securely established:

Party A Shared Secret = V_(A) × P_(B) =V_(A) × (V_(B) × G) Party B Shared Secret = V_(B) × P_(A) =V_(B) × (V_(A) × G)

As EC arithmetic is commutative, the shared secret is equivalent for both parties.

Secure Value Embedding in Elliptic Curve Public/Private Keys

It is possible to embed a message(value) into EC public/private keys. In order to apply this concept as a method for securely communication between two parties, the following parameters are required:

Parameter Details Base public The public key from which all value embedded keys P’ key P are derived EC Generator Elliptic Curve function such as secp256k1 which is G used by Bitcoin Shared Secret S As per the technique described above. Note that only the public keys from both parties need to be shared Range or set of Limits the possible values the receiver of a value n values v_1, embedded key needs to check. This is necessary as v_2, . . . , v_n embedding is a one directional operation which is computationally expensive. Value embedding The underlying Elliptic Curve formula which embeds formula M the value into a public key Embedding Value Method

A sending party can embed a value using a secure formula M such as:

V’ = V + HASH(value + S) value embedded private key P’ = P + HASH(value 

 S) × G value embedded public key where:

-   -   P is a base or initial public key     -   G is an Elliptic Curve function, such as secp256k1     -   x denotes elliptic curve multiplication by scalar; and     -   denotes elliptic curve addition.

The security of this method incorporates and embodies the following points:

-   -   The value embedded public key uses EC arithmetic which is one         directional and intractable to reverse     -   The hashing function is one directional and difficult to reverse     -   Shared Secret S is used as a hash salt. This means that even if         all other parameters are compromised, an attacker cannot simply         iterate through the possible values to work out the embedded         value. S is guaranteed to be secure unless the private keys are         compromised.         Value Extracting Method

The receiver of a value embedded in a public key can extract the value in linear time. This is done by calculating a value-embedded public key for each possible value until a match is found. This can be achieved by:

For each v in range v_0 to v_n //In this particular script, v_0, v_1, ..., v_n is a range, rather than a set v′ = M(v, P, S, G) //M is the formula using EC arithmetic to embed v If v′ equals P’ Exit loop //v is the embedded value Blockchain Transaction Outputs Conditional on Inputs

This section presents a method for constructing a blockchain transaction where the outputs are conditioned on the inputs. This is based off knowledge about using signature types SIGHASH_ALL and SIGHASH_NONE which is available in the public domain: https://bitcoin.org/en/developer-guide#signature-hash-types

Signature Types

Bitcoin signatures are a hash of select parts of a Transaction. The parts that are selected are determined by the signature hash type. The signature secures the hashed parts as any modification will yield a different signature thus showing tampering. FIG. 1 shows an example transaction and the parts which are hashed with SIGHASH_ALL and SIGHASH_NONE. It should be noted that, when signing an input, the scriptSigLen & scriptSig of all other inputs are replaced with empty scripts.

Transaction Construction Method

-   -   1. The blockchain Transaction is created, and inputs are added         by all entities     -   2. All entities, apart from Owner, sign their input with         SIGHASH_NONE (this locks in the inputs so they cannot be         modified)     -   3. The Owner determines the output, and updates the transaction     -   4. The Owner signs its input with SIGHASH_ALL, the transaction         is now complete (this locks in both the inputs and the outputs)         Implementing an Externally Evaluated Function as a Blockchain         Transaction

The invention can combine all of the previously described concepts/methods.

Key aspects include are:

-   -   Input values to the function can be embedded in public keys         which are communicated as transaction inputs     -   The Owner of the function (i.e. the resource which is         responsible for executing the function) can interrogate the         transaction prior to publication on the Blockchain to implement         the function     -   The Owner of the function alone can modify the output address of         the transaction prior to completion to represent the output of         the function         Key Terms

For clarity the following terms will be used throughout to define the implementation and use cases of the present invention.

Name Type Controller The owner of the transaction representing a function. This is the only entity which can update the transaction's outputs even after inputs are signed Input One of the entities which adds an input containing Sources a Value Embedded PubKey to the transaction Value This is a cryptographic (Bitcoin) Public Key Embedded which has a value embedded in it with PubKey Elliptic Curve arithmetic PubKey A protocol where: The sender and receiver agrees on the Protocol set of parameters and embedding + extracting method as described above in the section relating to Secure Value Embedding in Elliptic Curve Public/Private Keys A sender communicates the Value Embedded PubKey through one of the input unlocking scripts in the receiver's transaction (the sender must let the receiver know which key has a value embedded) Implementation

-   -   1. A Controller establishes a PubKey Protocol with each Input         Source, as shown in FIG. 2 a.     -   2. Input Source has a value to communicate and calculates a         Value Embedded PubKey according to its PubKey Protocol, as shown         in FIG. 2b     -   3. Input Source uses the Value Embedded PubKey to create a         locking script which is used in one of the outputs of an         Intermediate Transaction (created by Input Source). The         Intermediate Transaction is submitted to the blockchain; it is         not important whether the locking script is P2PKH or P2SH. This         is shown in FIG. 2 c.     -   4. Transaction is created and unsigned input from Controller and         each Input Source are added; see FIG. 2d         -   a. The inputs by each Input Source references their             intermediate transaction, specifically the output with the             Value Embedded PubKey         -   a. It is not important whether this transaction or the             intermediate transactions are created first (i.e. order of             steps 2-3), as long as all inputs are added to this             transaction before step 4         -   b. It is not important who creates the transaction as long             as all parties involved can modify it     -   5. Every Input Source signs their input to the transaction with         signature hash type SIGHASH_NONE         -   a. This locks in the inputs, but leaves the outputs free to             be modified         -   b. It is not important how each Input Source is             informed/checks when all inputs are added     -   6. Controller takes the Value Embedded PubKey from each Input         Source's unlocking scripts in the transaction and extracts the         value embedded based on the associated PubKey Protocol; see FIG.         2 f.         -   a. The value extraction is done externally to the bitcoin             transaction         -   b. It is not important how the Controller is informed/checks             when all inputs by Input Sources are signed     -   7. Controller applies the function to the extracted values, and         modifies the transaction output(s) based on the result; see FIG.         2 g.         -   a. The function is applied external to the bitcoin             transaction     -   8. Controller signs its input using SIGHASH_ALL, and submits the         transaction to the blockchain; see FIG. 2 h.

Use Case Example 1: XOR Logic Gate

We now present, for the purposes of illustration, an example use cases which implements present invention by using a (Bitcoin) transaction to represent an XOR logic gate with two input sources. Consider the following scenario.

Alice is a self-taught trader who sees an opportunity to make extra income by trading Company XYZ Stock Options. She opens an account with a particular Online Stock Exchange which accepts payments in Bitcoin. Alice develops a simple Trading Bot, Share Prices Bot, and a Market Index Value Bot. (Each “bot” is a computer-based resource arranged to perform an automated task or process).

The Share Prices Bot and Market Index Value Bot are setup such that:

-   -   Both bots record opening value range of the stock market     -   Both bots communicate with the Trading Bot if one of the bots         sees a value change to another range during the day     -   Share Prices Bot scrapes:         -   Price of Share XYZ—{P1, P2, . . . , P10}*     -   Market Index Value Bot scrapes:         -   Market Index Value—{M1, M2, . . . , M5}*             * represent ranges of values in ascending order. P1<P2< . .             . <P10

The Trading Bot buys call and put options based on the market data it receives:

Input Input (Price of Share (Market Index XYZ) Value) Output p ∈ {P7, P8, P9, m ∈ {M1, False - Buy Put Option - High P10} - True M2} - True prices but weak market. Alice predicts price will drop p ∈ {P7, P8, P9, m ∈ {M1, True - Buy Call Option - High P10} - True M2} - False prices but strong market. Alice predicts price will rise p ∈ {P7, P8, P9, m ∈ {M1, True - Buy Call Option - Low P10} - False M2} - True prices and weak market. Alice predicts price will rise p ∈ {P7, P8, P9, m ∈ {M1, False - Buy Put Option - Low P10} - False M2} - False prices and strong market. Alice predicts price will drop

It is important to note that the Share Prices Bot and Market Index Bot only send market data, they do not know the strategy.

Existing Set Up

-   -   Alice has given Trading Bot private/public key pair A which has         SBTC     -   Alice has given Share Prices Bot private/public key pair X which         has 1BTC     -   Alice has given Market Index Value Bot private/public key pair Y         which has 1BTC     -   Exchange takes payments for Put and Call Options at public key         E_PUT and E_CALL respectively         Steps:     -   1. Alice runs all three bots for the first time:         -   a. Trading Bot establishes a PubKey Protocol with Share             Prices Bot with the following parameters:

Parameter Details Base public key Public Key X EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key X) × G Trading Bot and Share Prices Bot calculates this by using each other's public key Range or set of P1, P2, . . . , P10 values Value embedding X’ = X + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Trading Bot establishes a PubKey Protocol with Market             Index Value Bot with the following parameters:

Parameter Details Base public key Public Key Y EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key Y) × G Trading Bot and Market Index Value Bot calculates this by using each other's public key Range or set of M1, M2, . . . , M5 values Value embedding Y’ = Y + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Share Prices Bot and Market Index Value Bot records the         opening value range of the stock market as P5 and M3         respectively     -   3. Market Index Value Bot detects a change to M2. Both bots         calculate a Value Embedded PubKey to send to Trade Bot         -   a. Stock Price Bot:             X′=X+SHA256(P5             S)×G  i.         -   b. Market Index Value Bot:             Y′=Y+SHA256(M2             S)×G  i.     -   4. Both bots create and submit to the blockchain an Intermediate         Transaction with an output which requires a P2PKH unlocking         script with their Value Embedded PubKey;         -   See FIG. 3 for the Stock Price Bot's Intermediate             Transaction. Note that output 1 requires the unlocking             script with Value Embedded PubKey X′; Output 2 is change             back to Stock Price Bot         -   See FIG. 4 for the Market Index Value Bot's Intermediate             Transaction; Note that output 1 requires the unlocking             script with Value Embedded PubKey Y′; Output 2 is change             back to Stock Price Bot     -   5. Both bots send Trading Bot an unsigned transaction input         containing their respective Value Embedded PubKey         -   See FIG. 5a for the Stock Price Bot's Input         -   See FIG. 5b for the Market Index Value Bot's Input     -   6. See FIG. 6: Trading Bot creates the transaction representing         an XOR gate including the transaction inputs received from Stock         Price Bot and Market Index Value Bot     -   7. See FIG. 7: Trading Bot informs Stock Price Bot and Market         Index Value Bot of the transaction's storage/access details and         requests them to sign their input.         -   a. Both bots sign with SIGHASH_NONE, locking in the inputs     -   8. Trading Bot takes <PubKey X′> from the unlocking script, and         calculates Value Embedded PubKeys for P1, P2, . . . , P10 until         it finds a matching pubkey with P5     -   9. Trading Bot takes <PubKey Y′> from the unlocking script, and         calculates Value Embedded PubKeys for M1, M2, . . . , M5 until         it finds a matching pubkey with M2     -   10. Trading Bot takes applies the XOR logic gate to the values,         and determines that it should buy a call option         -   a. P5∈{P7, P8, P9, P10} XOR M2∈{M1, M2}         -   b. FALSE XOR TRUE         -   c. TRUE—buy call option     -   11. See FIG. 8: Trading Bot updates the output to send SBTC to         E_PUT, signs its output with SIGHASH_ALL, and submits to the         blockchain

Use Case Example 2: AND Logic Gate

Implements the Bitcoin transaction to represent an AND logic gate with two input sources Imagine a bank that contains a vault with a dual control (dual custody) electronic combination lock. No single person is given both combinations, the simultaneous presence of two bank managers is required to open the door. If both combinations are correctly entered at the same time (‘1111’ and ‘2222’), the vault door will unlock, otherwise the vault alarm is activated. This is an implementation of an AND gate.

The whole system consists of 4 entities: Combination Lock A, Combination Lock B, Controller, and Vault

AND Logic in Controller: Combination A==‘1111’ AND Combination B==‘2222’

Input Signal Input Signal from Combination from Combination Controller Output Signal Lock A Lock B AND from Controller to Controller to Controller Logic to Vault 1111 2222 TRUE Unlock Door 1111 All other 4 digit FALSE Activate Alarm combinations besides 2222 All other 4 digit 2222 FALSE Activate Alarm combinations besides 1111 All other 4 digit All other 4 digit FALSE Activate Alarm combinations combinations besides 1111 besides 2222

It should be noted that all logic evaluation is performed by the Controller. The Combination Locks simply sends the 4 digit code but does not evaluate whether the code is TRUE or FALSE.

Existing Setup

-   -   Combination Lock A owns private/public key pair A which has 1BTC     -   Combination Lock B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Vault owns private/public key pair V_DOOR and V_ALARM         Steps:     -   1. When the system was first installed, Controller established a         PubKey Protocol with Combination Lock A and Combination Lock B         to allow secure communication of signals:         -   a. Controller & Combination Lock A's PubKey Protocol             parameters:

Parameter Details Base public key Public Key A (owned by Combination Lock A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Combination Lock A calculates this by using each other's public key Range or set of 0000, 0001, . . . , 9998, 9999 values Value embedding PubKey A’ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Combination Lock B's PubKey Protocol             parameters:

Parameter Details Base public key Public Key B (owned by Combination Lock B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Combination Lock B calculates this by using each other's public key Range or set of 0000, 0001, . . . , 9998, 9999 values Value embedding PubKey B′ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Bank Managers simultaneously enter their respective 4 digit         code (1111 and 2222) into Combination Lock A and Combination         Lock B. Each Combination Lock embeds their 4 digit code into a         Value Embedded PubKey (PubKey A′ and PubKey B′)         -   c. Combination Lock A:             PubKey A′=PubKey A+SHA256(‘1111’             S)×G  i.         -   d. Combination Lock B:             PubKey B′=PubKey B+SHA256(‘2222’             S)×G  i.     -   3. Both Combination Locks create and submit to the blockchain a         Bitcoin transaction (Intermediate Transaction) with an output to         their respective Value Embedded PubKey         -   a. Combination Lock A's Intermediate Transaction: See FIG. 9             -   Output 1—the input spending this output will communicate                 PubKey A′ to the Controller             -   Output 2—change back to Combination Lock A's public key                 A         -   b. Combination Lock B's Intermediate Transaction: See FIG.             10             -   Output 1—the input spending this output will communicate                 PubKey B′ to the Controller             -   Output 2—change back to Combination Lock B's public key                 B     -   4. Both Combination Locks create an unsigned Bitcoin transaction         input which spends output 1 of their respective Intermediate         Transaction. They send this input to the Controller—See FIG. 11         for         -   a. Combination Lock A's transaction input         -   b. Combination Lock B's transaction input:     -   5. Controller uses the Bitcoin transaction inputs from the         Combination Locks and creates a Bitcoin transaction representing         an AND gate (AND Gate Transaction). This transaction includes an         input from the Controller itself, so that it alone can modify         the outputs. See FIG. 12     -   6. Controller requests for Combination Lock A and Combination         Lock B to sign their respective input in the AND Gate         Transaction using SIGHASH_NONE. This locks in the inputs, while         still allowing the outputs to be modified—See FIG. 13     -   7. Controller uses its PubKey Protocol with Combination Lock A         to calculate a Value Embedded PubKey for each 4 digit         combination 0000, 0001, . . . , 9998, 9999 until it finds one         which matches PubKey A′         -   a. Controller finds that ‘1111’ produces the same Value             Embedded PubKey as PubKey A′     -   8. Controller uses its PubKey Protocol with Combination Lock B         to calculate a Value Embedded PubKey for each 4 digit         combination 0000, 0001, . . . , 9998, 9999 until it finds one         which matches PubKey B′         -   a. Controller finds that ‘2222’ produces the same Value             Embedded PubKey as PubKey B′     -   9. Controller applies the AND gate logic to the combinations:         -   a. Combination A=‘1111’ AND Combination B=‘2222’         -   b. TRUE AND TRUE         -   c. TRUE—send signal to V_DOOR to unlock door     -   10. Controller updates AND Gate Transaction's output to send         signal to V_DOOR and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain: See FIG. 14     -   11. Vault upon seeing a transaction output to V_DOOR, unlocks         the vault door

Use Case Example 3: IMPLY Logic Gate

In this example we implement the Bitcoin transaction to represent an IMPLY logic gate with two input sources. Imagine a plane with two switches, Switch A which turns on/off manual mode, and Switch B which turns on/off the landing gear extending system. If Switch A is off (auto-landing), the landing gear is always extended regardless of Switch B. Switch A is on (manual mode), the landing gear is extended based on Switch B. This is an implementation of an IMPLY gate. The whole system consists of 4 entities: Switch A, Switch B, Controller, and Landing Gear.

IMPLY Logic in Controller: Switch A==On IMPLY Switch B==On

Output Signal from Input Signal Input Signal Controller Controller to from Switch A from Switch B IMPLY Landing Gear to Controller to Controller Logic Extending System Off Off TRUE Extend (auto-mode, always extend) Off On TRUE Extend (auto-mode, always extend) On Off FALSE Retract (manual-mode, extend based on switch B) On On TRUE Extend (manual-mode, extend based on switch B)

All logic evaluation is performed by the Controller. The Switches simply send their state

Existing Set Up

-   -   Switch A owns private/public key pair A which has 1BTC     -   Switch B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Landing Gear Extending System owns private/public key pair         L_EXTEND and L_RETRACT         Steps     -   1. When the system was first installed, Controller established a         PubKey Protocol with Switch A and Switch B to allow secure         communication of signals:         -   a. Controller & Switch A's PubKey Protocol parameters:

Parameter Details Base public key Public Key A (owned by Switch A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Switch A calculates this by using each other's public key Range or set of On, Off values Value embedding PubKey A′ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Switch B's PubKey Protocol parameters:

Parameter Details Base public key Public Key B (owned by Switch B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Switch B calculates this by using each other's public key Range or set of On, Off values Value embedding PubKey B’ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Manual Mode is currently engaged (Switch A is on), and the         Landing Gears are retracted (Switch B is off).     -   3. The Pilot prepares for landing and turns Switch A off         (auto-landing). Each Switch embeds their state into a Value         Embedded PubKey (PubKey A′ and PubKey B′)         -   a. Switch A:             PubKey A′=PubKey A+SHA256(Off             S)×G  i.         -   b. Switch B:             PubKey B′=PubKey B+SHA256(Off             S)×G  i.     -   4. Both Switches create and submit to the blockchain a Bitcoin         transaction (Intermediate Transaction) with an output to their         respective Value Embedded PubKey         -   a. Switch A's Intermediate Transaction: See FIG. 15             -   Output 1—the input spending this output will communicate                 PubKey A′ to the Controller             -   Output 2—change back to Switch A's public key A         -   c. Switch B's Intermediate Transaction: see FIG. 16             -   Output 1—the input spending this output will communicate                 PubKey B′ to the Controller             -   Output 2—change back to Switch B's public key B     -   5. Both Switches create an unsigned Bitcoin transaction input         which spends output 1 of their respective Intermediate         Transaction. They send this input to the Controller: see FIG. 17         for         -   a. Switch A's transaction input         -   b. Switch B's transaction input     -   6. Controller uses the Bitcoin transaction inputs from the         Switches and creates a Bitcoin transaction representing an IMPLY         gate (IMPLY Gate Transaction). This transaction includes an         input from the Controller itself, so that it alone can modify         the outputs. See FIG. 18     -   7. Controller requests for Switch A and Switch B to sign their         respective input in the IMPLY Gate Transaction using         SIGHASH_NONE. This locks in the inputs, while still allowing the         outputs to be modified—See FIG. 19     -   8. Controller uses its PubKey Protocol with Switch A to         calculate a Value Embedded PubKey for On and Off, to find a         match with PubKey A′         -   a. Controller finds that Off produces the same Value             Embedded PubKey as PubKey A′     -   9. Controller uses its PubKey Protocol with Switch A to         calculate a Value Embedded PubKey for On and Off, to find a         match with PubKey B′         -   a. Controller finds that Off produces the same Value             Embedded PubKey as PubKey B′     -   10. Controller applies the IMPLY gate logic:         -   a. Switch A==On IMPLY Switch B==On         -   b. Off==On IMPLY Off==On         -   c. FALSE IMPLY FALSE         -   d. TRUE—send signal to L_EXTEND to extend the landing gear     -   11. Controller updates IMPLY Gate Transaction's output to send         signal to L_EXTEND and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain: See FIG. 20     -   12. Landing Gear Extending System upon seeing a transaction         output to L_EXTEND, turns on

Use Case Example 4: NAND Logic Gate

In this example, we implements the Bitcoin transaction to represent an NAND logic gate with two input sources. In a car each door typically has a switch that opens when the door is open, and if one or more doors are open a warning light is switched on to warn the driver. This is an implementation of a NAND gate. The whole system consists of 4 entities: Switch A, Switch B, Controller, and Light. Both Switches send a signal to the Controller when one of them changes state

NAND Logic in Controller: Switch A=Closed NAND Switch B=Closed

Input Signal Input Signal Controller Output Signal from Switch A from Switch B NAND from Controller to Controller to Controller Logic to Light Open Open TRUE Turn On Open Closed TRUE Turn On Closed Open TRUE Turn On Closed Closed FALSE Turn Off

All logic evaluation is performed by the Controller. The Switches simply sends their open or closed state to the Controller.

Existing Set Up

-   -   Switch A owns private/public key pair A which has 1BTC     -   Switch B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Light owns private/public key pair L_TURNON and L_TURNOFF         Steps:     -   1. When the system was first installed, Controller established a         PubKey Protocol with Switch A and Switch B to allow secure         communication of signals:         -   a. Controller & Switch A's PubKey Protocol parameters:

Parameter Details Base public key Public Key A (owned by Combination Lock A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Switch A calculates this by using each other's public key Range or set of Open, Closed (mapped to any unique pair of values numbers) Value embedding PubKey A’ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Switch B's PubKey Protocol parameters:

Parameter Details Base public key Public Key B (owned by Combination Lock B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Switch B calculates this by using each other's public key Range or set of Open, Closed (mapped to any unique pair of values numbers) Value embedding PubKey B’ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Switch A detects that its door has changed from closed         opened, while Switch B detects that its door remains closed.         Each Switch embeds their respective state (Open and Close) into         a Value Embedded PubKey (PubKey A′ and PubKey B′)         -   a. Switch A:             PubKey A′=PubKey A+SHA256(‘Open’             S)×G  i.         -   b. Switch B:             PubKey B′=PubKey B+SHA256(‘Close’             S)×G  i.     -   3. See FIG. 21a and FIG. 21b . Both Switches create and submit         to the blockchain a Bitcoin transaction (Intermediate         Transaction) with an output to their respective Value Embedded         PubKey         -   a. Switch A's Intermediate Transaction: FIG. 21a             -   Output 1—the input spending this output will communicate                 PubKey A′ to the Controller             -   Output 2—change back to Switch A's public key A     -   b. Switch B's Intermediate Transaction: FIG. 21b         -   Output 1—the input spending this output will communicate             PubKey B′ to the Controller         -   Output 2—change back to Switch B's public key B     -   4. Both Switches send the Controller an unsigned Bitcoin         transaction input which spends output 1 of their respective         Intermediate Transaction. See FIG. 22 for         -   a. Switch A's transaction input:         -   b. Switch B's transaction input:     -   5. Controller uses the Bitcoin transaction inputs from the         Switches and creates a Bitcoin transaction representing a NAND         gate (NAND Gate Transaction). This transaction includes an input         from the Controller itself, so that it alone can modify the         outputs. See FIG. 23     -   6. Controller requests for Switch A and Switch B to sign their         respective input in the NAND Gate Transaction using         SIGHASH_NONE. This locks in the inputs, while still allowing the         outputs to be modified. See FIG. 24     -   7. Controller uses its PubKey Protocol with Switch A to         calculate a Value Embedded PubKey for each state Open and Close.         -   a. Controller finds that ‘Open’ produces the same Value             Embedded PubKey as PubKey A′         -   b. Controller uses its PubKey Protocol with Switch B to             calculate a Value Embedded PubKey for each state Open and             Close             -   Controller finds that ‘Close’ produces the same Value                 Embedded PubKey as PubKey B′     -   8. Controller applies the NAND gate logic to the switch states:         -   a. Switch A=Closed NAND Switch B=Closed         -   b. FALSE NAND TRUE         -   c. TRUE—send signal to L_TURNON to turn on light     -   9. Controller updates NAND Gate Transaction's output to send         signal to L_TURNON and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain. See FIG. 25.     -   10. Light upon seeing a transaction output to L_TURNON, turns on

Use Case Example 5: NONIMPLY Logic Gate

In the example we implement the Bitcoin transaction to represent a NONIMPLY logic gate with two input sources. Imagine a smart driveway lighting system which has Sensor A which detects the presence of a car, and Switch B which turns on/off manual only mode. If Sensor A does not detect a car, the driveway light is off. If Sensor A detects a car, it automatically turns on the driveway light if Switch B manual mode is off. This is an implementation of a NONIMPLY gate. The whole system consists of 4 entities: Sensor A, Switch B, Controller, and Driveway Light

NONIMPLY Logic in Controller: Sensor A==‘Car’ IMPLY Switch B==‘Manual On’

Output Signal Input Signal Input Signal Controller from Controller from Switch A from Switch B NONIMPLY to Driveway to Controller to Controller Logic Light No Car Manual Off FALSE Turn Off Driveway Light No Car Manual On FALSE Turn Off Driveway Light Car Manual Off TRUE Turn On Driveway Light Car Manual On FALSE Turn Off Driveway Light

All logic evaluation is performed by the Controller. The Sensor and Switch simply sends their state.

Existing Setup:

-   -   Sensor A owns private/public key pair A which has 1BTC     -   Switch B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Driveway Light owns private/public key pair L_ON and L_OFF         Steps:     -   1. When the system was first installed, Controller established a         PubKey Protocol with Sensor A and Switch B to allow secure         communication of signals:         -   a. Controller & Sensor A's PubKey Protocol parameters:

Parameter Details Base public key Public Key A (owned by Switch A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Sensor A calculates this by using each other's public key Range or set of Car, No Car values Value embedding PubKey A’ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Switch B's PubKey Protocol parameters:

Parameter Details Base public key Public Key B (owned by Switch B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Switch B calculates this by using each other's public key Range or set of Manual On, Manual Off values Value embedding PubKey B’ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Sensor A currently detects no cars and Switch B has manual         mode turned off.     -   3. Sensor A detects a car on the driveway. The Sensor and Switch         embeds their state into a Value Embedded PubKey (PubKey A′ and         PubKey B′)         -   a. Sensor A:             PubKey A′=PubKey A+SHA256(Car             S)×G  i.         -   b. Switch B:             PubKey B′=PubKey B+SHA256(Manual Off             S)×G  i.     -   4. Both Switches create and submit to the blockchain a Bitcoin         transaction (Intermediate Transaction) with an output to their         respective Value Embedded PubKey         -   a. Sensor A's Intermediate Transaction: FIG. 26 a             -   Output 1—the input spending this output will communicate                 PubKey A′ to the Controller             -   Output 2—change back to Switch A's public key A     -   b. Switch B's Intermediate Transaction: FIG. 26b         -   Output 1—the input spending this output will communicate             PubKey B′ to the Controller         -   Output 2—change back to Switch B's public key B     -   5. Sensor A and Switch B create an unsigned Bitcoin transaction         input which spends output 1 of their respective Intermediate         Transaction. They send this input to the Controller. See FIG. 27         for         -   a. Sensor A's transaction input:         -   b. switch B's transaction input:     -   6. Controller uses the Bitcoin transaction inputs from the         Sensor and Switch to create a Bitcoin transaction representing a         NONIMPLY gate (NONIMPLY Gate Transaction). This transaction         includes an input from the Controller itself, so that it alone         can modify the outputs. See FIG. 28.     -   7. Controller requests for Sensor A and Switch B to sign their         respective input in the NONIMPLY Gate Transaction using         SIGHASH_NONE. This locks in the inputs, while still allowing the         outputs to be modified. See FIG. 29.     -   8. Controller uses its PubKey Protocol with Sensor A to         calculate a Value Embedded PubKey for Car and No Car, to find a         match with PubKey A′         -   a. Controller finds that Car produces the same Value             Embedded PubKey as PubKey A′     -   9. Controller uses its PubKey Protocol with Switch A to         calculate a Value Embedded PubKey for Manual On and Manual Off,         to find a match with PubKey B′         -   a. Controller finds that Manual Off produces the same Value             Embedded PubKey as PubKey B′     -   10. Controller applies the NONIMPLY gate logic:         -   a. Sensor A==‘Car’ NONIMPLY Switch B==‘Manual On’         -   b. ‘Car’==‘Car’ NONIMPLY ‘Manual Off’==‘Manual On’         -   c. TRUE IMPLY FALSE         -   d. TRUE—send signal to L_ON to turn on driveway light     -   11. Controller updates NONIMPLY Gate Transaction's output to         send signal to L_ON and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain. See FIG. 30.     -   12. Driveway light upon seeing a transaction output to L_ON,         turns on

Use Case Example 6: NOT Logic Gate

In this example we implement the Bitcoin transaction to represent a NOT logic gate with one input source. Imagine that the Crown Jewels in the Tower of London are displayed to millions of visitors every year. Imagine that the Imperial State Crown sits upon a pressure sensitive switch that is normally closed. Placing the crown on the switch arms the alarm. Removing the crown from the switch activates the alarm. This is an implementation of a NOT gate. The whole system consists of a controller, a switch, and an alarm. The Switch sends a signal to the Controller when it changes state.

NOT Logic in Controller: NOT Switch=Closed

Output Signal Signal from Controller NOT from Controller Switch logic to Alarm Closed False Activate Alarm Open True Arm Alarm Existing Setup

-   -   Switch owns private/public key pair X which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Alarm owns private/public key pairs A_Activate and A_Arm         Steps:     -   1. During installation, Controller and Switch establishes a         PubKey Protocol with the following parameters:

Parameter Details Base public key Public Key X (uses Switch's public key) EC Generator G secp256k1 Shared Secret S (Private Key C) × (Private Key X) × G Controller and Switch calculates this by using each other's public key Range or set of True, False values Value embedding PubKey X’ = PubKey X + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Switch is initially in closed state (crown is on the switch)     -   3. Switch detects a change when the crown is removed. Switch         embeds signal ‘false’ into a Value Embedded PubKey (PubKey X′)         PubKey X′=PubKey X+SHA256(‘false’         S)×G  a.     -   4. Switch creates and submits to the blockchain an Intermediate         Transaction with an output to its Value Embedded PubKey. See         FIG. 31         -   Output 1—the input spending this output will communicate             PubKey X′ to the Controller         -   Output 2—change back to Switch X's public key A     -   5. Switch sends Controller an unsigned Bitcoin transaction input         spending Output 1 of the Intermediate Transaction. See FIG. 32     -   6. Controller creates a Bitcoin transaction representing an NOT         gate (NOT Gate Transaction) including the Bitcoin transaction         input received from Switch. See FIG. 33     -   7. Controller requests Switch to sign its input in NOT Gate         Transaction so that it is locked in         -   a. Switch signs with SIGHASH_NONE, preventing it from being             modified:

FIG. 34

-   -   8. Controller calculates Value Embedded PubKey for ‘true’ and         ‘false’, and compares it with the Value Embedded PubKey (PubKey         X′) from the unlocking script. It finds a match with ‘false’     -   9. Controller applies the NOT gate to the value ‘false’, and         determines that it should send a signal to Activate Alarm         (A_ACTIVATE)     -   10. Controller updates NOT Gate Transaction's output to send a         signal to A_ACTIVATE and change back to its own public key C. It         then signs is input with SIGHASH_ALL, and submits to the         blockchain. See FIG. 35         -   Output 1—Signal to Activate Alarm         -   Output 2—Change back to Controller's public key C     -   11. Alarm upon seeing a transaction output to A_ACTIVATE,         activates

Use Case Example 7: OR Logic Gate

Implements the Bitcoin transaction to represent an OR logic gate with two input sources Consider a building with an automated airflow system which uses an internal and external temperature sensor. The temperature sensors reads integer degrees Celsius from −30 to 50. If the internal temperature is above 21 or the external temperature is above 25, the airflow system expels cool air, otherwise the airflow system expels warm air. This is an implementation of an OR gate. The whole system consists of 4 entities: Temp. Sensor A, Temp. Sensor B, Controller, and Airflow System. Both sensors send a signal to the controller when either one detects a change in temperature.

OR Logic in Controller: Temp. A>21 OR Temp. B>25

Output Signal Input Signal from Input Signal from Controller from Controller Temp. Sensor A Temp. Sensor B OR to Airflow to Controller to Controller Logic System 21, 22, . . . , 49, 50 26, 27, . . . , 49, 50 TRUE Cool Air 21, 22, . . . , 49, 50 −30, −29, . . . , 24, 25 TRUE Cool Air −30, −29, . . . , 19, 20 26, 27, . . . , 49, 50 TRUE Cool Air −30, −29, . . . , 19, 20 −30, −29, . . . , 24, 25 FALSE Warm Air

All logic evaluation is performed by the Controller. The Temp. Sensors simply sends the temperature reading but does not evaluate whether it is hot or cold.

Existing Setup

-   -   Temp. Sensor A owns private/public key pair A which has 1BTC     -   Temp. Sensor B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Airflow System owns private/public key pair S_COOL and S_WARM         Steps     -   1. When the system was first installed, Controller established a         PubKey Protocol with Temp. Sensor A and Temp. Sensor B to allow         secure communication of signals:         -   a. Controller & Temp. Sensor A's PubKey Protocol parameters:

Parameter Details Base public key Public Key A (owned by Temp. Sensor A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Temp. Sensor A calculates this by using each other's public key Range or set of −30, −29, . . . , 49, 50 values Value embedding PubKey A’ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Temp. Sensor B's PubKey Protocol parameters:

Parameter Details Base public key Public Key B (owned by Temp. Sensor B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Temp. Sensor B calculates this by using each other's public key Range or set of −30, −29, . . . , 49, 50 values Value embedding PubKey B’ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. Temp. Sensor A currently reads 21, and Temp. Sensor B reads         27     -   3. Temp. Sensor A detects a change from 21 to 20. Each Temp.         Sensor embeds their reading into a Value Embedded PubKey (PubKey         A′ and PubKey B′)         -   a. Temp. Sensor A:             PubKey A′=PubKey A+SHA256(20             S)×G  i.         -   b. Temp. Sensor B:             PubKey B′=PubKey B+SHA256(27             S)×G  i.     -   4. Both Temp. Sensors create and submit to the blockchain a         Bitcoin transaction (Intermediate Transaction) with an output to         their respective Value Embedded PubKey     -   a. Temp. Sensor A's Intermediate Transaction: FIG. 36a         -   Output 1—the input spending this output will communicate             PubKey A′ to the Controller         -   Output 2—change back to Temp. Sensor A's public key A     -   b. Temp. Sensor B's Intermediate Transaction: FIG. 36 b         -   Output 1—the input spending this output will communicate             PubKey B′ to the Controller         -   Output 2—change back to Temp. Sensor B's public key B     -   5. Both Temp. Sensor create an unsigned Bitcoin transaction         input which spends output 1 of their respective Intermediate         Transaction. They send this input to the Controller. See FIG. 37         for         -   a. Temp. Sensor A's transaction input         -   b. Temp. Sensor B's transaction input     -   6. Controller uses the Bitcoin transaction inputs from the         Temperature Sensors and creates a Bitcoin transaction         representing an OR gate (OR Gate Transaction). This transaction         includes an input from the Controller itself, so that it alone         can modify the outputs. See FIG. 38     -   7. Controller requests for Temp. Sensor A and Temp. Sensor B to         sign their respective input in the OR Gate Transaction using         SIGHASH_NONE. This locks in the inputs, while still allowing the         outputs to be modified. See FIG. 39     -   8. Controller uses its PubKey Protocol with Temp. Sensor A to         calculate a Value Embedded PubKey for each temperature −30, −29,         . . . , 49, 50 until it finds one which matches PubKey A′         -   a. Controller finds that 20 produces the same Value Embedded             PubKey as PubKey A′     -   9. Controller uses its PubKey Protocol with Temp. Sensor B to         calculate a Value Embedded PubKey for each temperature −30, −29,         . . . , 49, 50 until it finds one which matches PubKey B′         -   a. Controller finds that 27 produces the same Value Embedded             PubKey as PubKey B′     -   10. Controller applies the OR gate logic to the temperature         readings:         -   a. Temp. A>21 OR Temp. B>25         -   b. 20>21 OR 27>25         -   c. FALSE OR TRUE         -   d. TRUE—send signal to S_COOL to expel cool air     -   11. Controller updates OR Gate Transaction's output to send         signal to S_COOL and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain. See FIG. 40     -   12. Airflow system upon seeing a transaction output to S_COOL,         expels cool air

Use Case Example 8: XNOR Logic Gate

In this example we implement the Bitcoin transaction to represent an XNOR logic gate with two input sources. Consider a production system which produces two items: cricket balls and cricket ball corks. Both items pass through the same quality control which has two scanners A and B. Scanner A gives a belief reading from 0, 5, 10, . . . , 95, 100% of whether the ball is red. Scanner B gives a belief reading from 0, 5, 10, . . . , 95, 100% of whether the ball has stitches. If a ball has both features, it is accepted as it is a normal cricket ball. If a ball has neither feature, it is also accepted as it is a cork. If a ball has only one of the features, it is rejected because it is a defect. This is an implementation of a XNOR gate.

The whole system consists of 4 entities: Scanner A, Scanner B, Controller, and Production System. Both detectors send a belief to the controller when either one detects a change. XNOR Logic in Controller: Scanner Belief A>90% XNOR Scanner Belief B>60% Detecting stitches is less accurate than detecting red, so a larger range of acceptable values is used for Scanner B.

Output Signal Input Signal Input Signal Controller from Controller from Scanner A from Scanner B XNOR to Prod. to Controller to Controller Logic System 0, 5, . . . , 75, 90% 0, 5, . . . , 55, 60% TRUE Accept 0, 5, . . . , 75, 90% 65, 70, . . . , 95, 100% FALSE Reject 95, 100% 0, 5, . . . , 55, 60% FALSE Reject 95, 100% 65, 70, . . . , 95, 100% TRUE Accept

All logic evaluation is performed by the Controller. The Scanners simply sends their belief reading but does not evaluate whether it is high enough to assume there is a fire.

Existing Setup

-   -   Scanner A owns private/public key pair A which has 1BTC     -   Scanner B owns private/public key pair B which has 1BTC     -   Controller owns private/public key pair C which has 1BTC     -   Production System owns private/public key pair S_ACCEPT and         S_REJECT         Steps:     -   1. When the system was first installed, Controller established a         PubKey Protocol with Scanner A and Scanner B to allow secure         communication of signals:         -   a. Controller & Scanner A's PubKey Protocol parameters:

Parameter Details Base public key Public Key A (owned by Scanner A) EC Generator G secp256k1 Shared Secret S (Private Key A) × (Private Key C) × G Controller & Scanner A calculates this by using each other's public key Range or set of 0, 5, . . . , 95, 100% values Value embedding PubKey A’ = PubKey A + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   -   b. Controller & Scanner B's PubKey Protocol parameters:

Parameter Details Base public key Public Key B (owned by Scanner B) EC Generator G secp256k1 Shared Secret S (Private Key B) × (Private Key C) × G Controller & Scanner B calculates this by using each other's public key Range or set of 0, 5, . . . , 95, 100% values Value embedding PubKey B’ = PubKey B + formula SHA256(value 

 S) × G Key Communicating Pay to Public Key Hash (P2PKH) Method

-   -   2. A ball passes through the scanners. Scanner A reads 100%         match. Scanner B reads 75% match.     -   3. Each Scanner embeds their reading into a Value Embedded         PubKey (PubKey A′ and PubKey B′)         -   a. Scanner A:             PubKey A′=PubKey A+SHA256(100%             S)×G  i.         -   b. Scanner B:             PubKey B′=PubKey B+SHA256(75%             S)×G  i.     -   4. Both Scanners create and submit to the blockchain a Bitcoin         transaction (Intermediate Transaction) with an output to their         respective Value Embedded PubKey         -   d. Scanner A's Intermediate Transaction: See FIG. 41a             -   Output 1—the input spending this output will communicate                 PubKey A′ to the Controller             -   Output 2—change back to Scanner A's public key A         -   e. Scanner B's Intermediate Transaction: See FIG. 41 b             -   Output 1—the input spending this output will communicate                 PubKey B′ to the Controller             -   Output 2—change back to Scanner B's public key B     -   5. Both Scanners create an unsigned Bitcoin transaction input         which spends output 1 of their respective Intermediate         Transaction. They send this input to the Controller. See FIG. 42         for         -   a. Scanner A's transaction input         -   c. Scanner B's transaction input     -   6. Controller uses the Bitcoin transaction inputs from the         Scanners and creates a Bitcoin transaction representing a XNOR         gate (XNOR Gate Transaction). This transaction includes an input         from the Controller itself, so that it alone can modify the         outputs. See FIG. 43     -   7. Controller requests for Scanner A and Scanner B to sign their         respective input in the XNOR Gate Transaction using         SIGHASH_NONE. This locks in the inputs, while still allowing the         outputs to be modified. See FIG. 44.     -   8. Controller uses its PubKey Protocol with Scanner A to         calculate a Value Embedded PubKey for each belief 0, 5, . . . ,         95, 100% until it finds one which matches PubKey A′         -   a. Controller finds that 100% produces the same Value             Embedded PubKey as PubKey A′     -   9. Controller uses its PubKey Protocol with Scanner B to         calculate a Value Embedded PubKey for each belief 0, 5, . . . ,         95, 100% until it finds one which matches PubKey B′         -   a. Controller finds that 75% produces the same Value             Embedded PubKey as PubKey B′     -   10. Controller applies the NOR gate logic to the temperature         readings:         -   a. Scanner Belief A>90% XNOR Scanner Belief B>60%         -   b. 100>60 XNOR 75>60         -   c. TRUE OR TRUE         -   d. TRUE—send signal to S_ACCEPT to accept the ball     -   11. Controller updates XNOR Gate Transaction's output to send         signal to S_ACCEPT and to give change back to itself. It then         signs its input with SIGHASH_ALL to lock in all inputs and         outputs, and submits to the blockchain. See FIG. 45.     -   12. The system upon seeing a transaction output to S_ACCEPT,         allows the ball to continue to packaging

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be capable of designing many alternative embodiments without departing from the scope of the invention as defined by the appended claims. In the claims, any reference signs placed in parentheses shall not be construed as limiting the claims. The word “comprising” and “comprises”, and the like, does not exclude the presence of elements or steps other than those listed in any claim or the specification as a whole. In the present specification, “comprises” means “includes or consists of” and “comprising” means “including or consisting of”. The singular reference of an element does not exclude the plural reference of such elements and vice-versa. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In a device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. 

The invention claimed is:
 1. A computer-implemented method of executing a portion of logic, the computer-implemented method comprising: generating a blockchain transaction comprising: at least one signed input that comprises a value; and at least one modifiable output; extracting the value from the at least one signed input and providing the value as an extracted value to a portion of logic to obtain a result, wherein the portion of logic represents an external system that is external to one or both of the blockchain transaction and a blockchain; using the result to modify the at least one modifiable output of the blockchain transaction such that the blockchain transaction represents the result; and modifying a state of the external system based on the modified at least one modifiable output of the blockchain transaction.
 2. The computer-implemented method according to claim 1, wherein the portion of logic is external to one or both of the blockchain transaction and the blockchain.
 3. The computer-implemented method according to claim 1, wherein a controller external to one or both of the blockchain transaction and the blockchain applies the portion of logic to the extracted value to obtain the result and communicates with the blockchain transaction to modify the at least one modifiable output of the blockchain transaction based on the result.
 4. The computer-implemented method according to claim 1, wherein the portion of logic is arranged to implement functionality of a logic gate.
 5. The method according to claim 4, wherein the logic gate is an AND, NOT, OR, NOR, XOR, IMPLY, NAND, NONIMPLY or XNOR gate.
 6. The computer-implemented method according to claim 1, further comprising submitting the blockchain transaction to the blockchain.
 7. The method according to claim 1, wherein the at least one signed input is provided to the blockchain transaction using an unlocking script.
 8. The method according to claim wherein the at least one signed input is signed using a signature hash type that renders the at least one signed input as non-modifiable.
 9. The method according to claim wherein the signature hash type is SIGHASH_NONE.
 10. The method according to claim wherein the blockchain transaction further comprises at least one unsigned input.
 11. The computer-implemented method according to claim 10, further comprising signing the at least one unsigned input after the at least one modifiable output has been modified.
 12. The method according to claim 11, wherein the at least one unsigned input is signed using a signature hash type that prevents modification of the whole blockchain transaction.
 13. The method according to claim 12, wherein the signature hash type is SIGHASH_ALL.
 14. The computer-implemented method according to claim 1, wherein the value is: embedded in a public key associated with the at least one signed input; and extracted from the public key so as to provide the extracted value to the portion of logic.
 15. The computer-implemented method according to claim 14, further comprising establishing and/or selecting a protocol and using the protocol to embed the value in the public key.
 16. The method according to claim 14, wherein the public key is used to create a locking script in an intermediate blockchain transaction.
 17. The computer-implemented method according to claim 16, further comprising submitting the intermediate blockchain transaction to the blockchain.
 18. The computer-implemented method according to claim 14, wherein the value is embedded in the public key by generating a new public key P′, wherein: P′=P+HASH(value

S)×G where: P is a base or initial public key; G is an elliptic curve function; x denotes elliptic curve multiplication by scalar; < denotes elliptic curve addition; and S is a shared secret.
 19. The computer-implemented method according to claim 18, further comprising generating a new private key corresponding to the new public key, wherein: new private key V′=V+HASH(value+S) where: V is a private key; and S is the shared secret.
 20. The method according to claim 14, wherein the value that is embedded in the public key is selected from a specified range of values.
 21. A computer-implemented system, comprising: at least one computer-based hardware resource, comprising: one or more processors; and memory storing executable instructions that, being executed by the one or more processors, cause the computer-implemented system to: generate a blockchain transaction comprising: at least one signed input comprising a value; and at least one modifiable output; extract the value from the at least one signed input and provide the value as an extracted value to a portion of logic to obtain a result, wherein the portion of logic represents an external system that is external to one or both of the blockchain transaction and a blockchain; use the result to modify the at least one modifiable output of the blockchain transaction such that the blockchain transaction represents the result; and modify a state of the external system based on the modified at least one modifiable output of the blockchain transaction; and the blockchain arranged to receive the blockchain transaction from the at least one computer-based hardware resource. 